1 Answer
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No

Unfortunately, superstitions about dice do not actually impact probability. However, a die can be unbalanced and thereby generate uneven results.

What your friend is experiencing is confirmation bias, wherein he is looking for bad rolls, and finds them, and then looks for good rolls and finds them. In order to falsify the claim of "exhausting bad rolls" have him, over the course of 5 sessions, track every single roll he makes in an excel spreadsheet or on a piece of paper. However, over those 5 sessions, use 5 different d20s. This should demonstrate if any given die is unbalanced and the falseness of his claim.

There may also be elements of positive bias(HP:MoR) as a component here, as your friend has an explanatory theory that seems to fit his observed confirmations and thereby has positive confirmation of that theory.

A third potential explanation is methods of rolling dice. There are techniques to make certain types of numbers more probable in a roll (this is cheating, of course...). Another test is to use a dice tower to generate the random numbers for rolls during a game, something I'd recommend anyways just because of the almost ritualistic elements of dropping dice into the top and awaiting their result (and not seeing the board disrupted due to errant dice.)

\$\begingroup\$"This should demonstrate if any given die is unbalanced and the falseness of his claim." Unless you're rolling bazillions of dice per session, you cannot have reasonable statistical significance.\$\endgroup\$
– R. Martinho FernandesJul 2 '11 at 18:36

\$\begingroup\$@Martinho If it does show bias during that time, then you've got either a real positive or a false positive. The die could be singled out for a larger sample size (say, five sessions) to see if the apparent poor randomness is an artefact of the small sample size, or you can just be pragmatic and pitch it in the "bad dice" box.\$\endgroup\$
– SevenSidedDieJul 2 '11 at 19:10

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\$\begingroup\$+1 thank you for debunking the myth. Curious, there's a difference between positive bias and confirmation bias?\$\endgroup\$
– LitheOhmApr 12 '13 at 7:42